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GLASS, BUGS, AND MUD

Running Head: GLASS, BUGS, AND MUD

Glass, Bugs, and Mud

Helping English Language Learners Be Successful in Mathematics

Jennifer Almendarez

Portland State University

Teacher as Researcher-CI 563

July 17, 2010
Helping English Language Learners Be Successful in Mathematics

I once read an article titled Using Data to Differentiate Instruction (Brimijoin, Marquisse, Tomlinson, 2003), which featured a teacher who had created an interesting form of self-assessment for her students. She referred to it as her car-windshield analogy. At the end of every lesson she would ask the students if their windshield was clear, if it was covered with bugs, or if it was completely muddy. This was their way of interpreting to her if they understood the material or not, and a great way for the teacher to adjust her instruction so that everyone could try and achieve that “clear windshield.”

I wish I had heard of this analogy before doing my student teaching. The focus of my Student Teaching II work sample was in the area of mathematics. Specifically, the goal of my instruction was to teach first graders various strategies of addition using math facts up to twelve. Throughout my unit, students were shown different ways that addition facts could be presented and they were given a variety of tools to help them solve problems.

I found my biggest challenge was trying to differentiate my instruction so that I could reach all levels of learners. Once I compared the results of my pre and post assessments, I noticed who was affected most by this challenge: English language learners. Although some of my English language learner students had made a little bit of growth, I was concerned about those who didn’t. This made me reflect on my teaching throughout the unit, and it got me to thinking about the following question: How can I differentiate my mathematics instruction to target English Language Learners and help them be successful?

In the greater scope of things, I do not want my students to fall behind because of a lack of quality instruction. This is especially important for our English Language Learners, as they are the fastest growing group in Northwest Schools (Jarrett, 1999, p. 6). I believe it is important for me as an elementary teacher to give all of my students an equal opportunity to be successful. My goal is to teach them in a way that builds their self-confidence and motivates them to continue learning, because eventually they are going to grow up and be contributing members of society. This is especially important for our ELL students. Statistics on mathematics achievement show that Latinos are significantly under- represented in all scientific and engineering careers in direct proportion to the amount of mathematics required for a particular job (Garrison & Mora, 1999). Our ELL students are not always Latinos, but in my case, I only had one student who wasn’t. This tells me that as teachers, we should try and tackle this problem early on.

So, how do I strive for the concept of that “clear windshield” for my English Language Learners? Well, I knew that since I was doing my work sample on mathematics, I would need to have a focus on the “language of math” so that I could make it more comprehensible for ELL students. This notion was backed up in my research such as in the Garrison and Mora article. These writers conclude that if new concepts are introduced in an unfamiliar language, students must struggle with two unknowns: the language and the concept (1999). However, it was really difficult for me at times to figure out how I was going to integrate this language piece into my lessons.

One suggestion, in relation to problem solving, is to have teachers introduce a discussion about the vocabulary and situational context of the problem, and then later help students break down the problem into “natural grammatical phrases” (Jarrett, 1999, p. 19). I found this recommendation to be very helpful because I did introduce some problem solving toward the end of my unit, and it was by far, some of the most challenging work I did with these students. However, I question how I could implement this exercise to first graders. I did my student teaching in the fall, and at that time, many of the students were not yet reading independently. I see how a lesson like this may have worked for the students later on in the year, but at the time that I did my student teaching, I’m not sure they would have been ready for it.

On the other hand, a suggestion like Jarrett’s tells me that maybe math and reading can be taught in one lesson instead of always teaching them as separate content. English language learners struggle with math lessons that rely heavily on reading (Cavanagh, 2005). Why not analyze the language in a math text as part of a reading assignment? I think this is something that can be adapted to teach first graders. Isn’t the goal of certain reading lessons to make sense out of text? Why not connect it to math in the process?

Another suggestion I found really helpful regarding the language of math, was something I easily could have done more with first graders. In their article, Garrison and Mora explain how words are easier to remember when students can see and touch the objects they represent while repeatedly hearing and saying new words (1999). After reading this, I immediately envisioned some of my lessons where I did do this and where doing this would have been more helpful. For example, one of the first addition concepts I taught was “counting on.” To help students with this strategy, I had them use linker cubes to touch as they were adding numbers together. They would start with a number, such as 4, and then had to touch the remaining cubes to “count on” and find their answer. It would have been more helpful for the ELL students however, if I had provided more explanation or practice (using a tangible manipulative) on what it really means to count on, because when it came time to do the post-assessment, I noticed that some of them still didn’t understand.

This idea of using manipulatives was something I really tried to do as often as I could throughout my math unit, because I knew it could help students be more successful. During my research however, I found a bit of information regarding the use of manipulatives that I hadn’t really thought of before. The article mentions how, when grouping students, teachers in differentiated classrooms should match materials to the specific instructional needs of groups (Tomlinson, Brighton, Hertberg, Callahan, Moon, Brimijoin, Conover, & Reynolds, 2003). This is a very interesting suggestion and one that I hadn’t really considered. As a teacher of first grade, one of my concerns was of course trying to keep things “fair” among the students. Thus, all students would receive the same manipulative that corresponded with lesson for that day. I understand now that maybe I should have really thought about if the manipulative was appropriate for every student or if I should have provided an alternative to certain students. Then again, to avoid singling out certain students, maybe I should have provided them with a variety of manipulatives (or at least a couple), and then they could choose which one they wanted to use during the lesson. This could have helped to keep them motivated as well.

Keeping students motivated was another suggestion that I found all throughout my research, and it’s something that I think I did a pretty good job of doing during my student teaching. For the most part, students seemed excited to learn and do their best during each lesson. However, some of the articles suggested things that I could have done that maybe would have specifically helped my ELL students be more successful. One idea suggests the following: “…teachers will want to place thematic units in the context of students’ everyday lives. This can be achieved by including real-world applications of key concepts; presenting ideas and organizing activities in the context of students’ home cultures; and by encouraging students to talk about their prior experiences and knowledge concerning the theme” (Jarrett, 1999, p. 15).

Although I felt successful at providing connections to the class as a whole, I had a difficult time trying to connect to my ELL students’ home culture in relation to mathematics. I could think of a million ways to bring culture into a reading lesson, but connecting it to math was a whole new ball game.

Unfortunately, my research did not provide me with any specifics on how to connect math with student cultures. The article talked extensively about the benefits of including the home language in lessons, but in my case this doesn’t suffice. Most of my ELL students, although they speak Spanish at home, do not have that academic piece in their native language. I did explain directions in Spanish if I felt the students really were not understanding, but I honestly don’t think it helped since these students have not been exposed to much of the math vocabulary at home.

The final suggestion I found during my research was in regards to assessing students. The research suggests that teachers will want to use a variety of assessment methods to provide a more complete picture of student progress and areas of need (Jarrett, 1999, p. 24). Formulating a well-suited assessment was hard for me during my work sample. I felt I needed to create a paper/pencil type exam so that I could tangibly show the assessment process for the purpose of my work sample. Although I read both assessments aloud to the class, the fact that the tests were still in the form of a paper-pencil type assessment, could have been a bit overwhelming for the ELL students. Had I had more time, I would have done more informal, even one-on-one assessments that required students to show me a solution, rather than just write it down on paper.

From my experience in my graduate studies, as well as in the classroom, it seems as though the task of differentiating instruction is one of the biggest challenges a teacher may face. I found this to be true in my research as well. One article states “a critical challenge for math teachers is finding a way to reach students with limited English skills without ignoring the needs of those already fluent in the language” (Cavanagh, 2005). However, I think many students that are native English speakers would benefit from many of the techniques I found throughout my research as well. I believe if I put them to practice, then I may be helping all of my students be successful.

There were many factors beyond my locus of control that could have affected the outcome of my work sample. Not having enough time with my students was probably the biggest hindrance to their learning. I never really felt like I was giving them as quality instruction as I could have if I had been given more time. There were many unexpected interruptions throughout the day and the ELL students were constantly being pulled out. This doesn’t change the fact, however, that there were many things I could have done better to help these students be more successful in mathematics. One day, when I have my own classroom, I will take my research findings and put them to good use. I will also seek out new research on relevant issues as they come up in my classroom. My hope is that, at the end of each day, I will have done everything in my power to help my students achieve that “clear windshield” in mathematics, so that they may be successful in my classroom and beyond.


References

Brimijoin K., Marquissee E., Tomlinson C. (2003). Using Data to Differentiate Instruction.

Educational Leadership, 60, 70-73.

Cavanagh, Sean. (2005). Math: The Not-So-Universal Language. Education Week, 24(42), 2

Garrison, Leslie and Mora, Jill Kerper. Adapting Mathematics Instruction for English Language

Learners: The Language-Concept Connections. Changing the Faces of Mathematics:

Perspectives on Latinos (March 1999): 35-48.

Jarrett, Denise. (1999). The Inclusive Classroom: Teaching Mathematics and Science to

English-Language Learners. It’s Just Good Teaching. Portland, OR: Northwest Regional

Educational Lab.

Tomlinson, C., Brighton C., Hertberg H., Callahan C., Moon T., Brimijoin K., Conover L.,

Reynolds T. (2003) Differentiating Instruction in Response to Student Readiness, Interest, and Learning Profile in Academically Diverse Classrooms: A Review of Literature

Journal for the Education of the Gifted, 27, 119-45.